Question

lim x tends to 3 1/x =1/3.is the statement true?​

Answer 1

Answer:

g(x)=

x

1

.

Limit of g(x) doesn't exist at x=0, but for

x→0

lim

f(x).g(x) and f(x)=x limit exists.

For option C,

Lets assume h(x)=f(x)+g(x),

Take limit on both sides as x→c

lim

x→c

h(x)=lim

x→c

(f(x)+g(x))

And it is given that lim

x→c

f(x) exists.

Using sum law of limits:

If lim

x→c

F(x) and lim

x→c

G(x) exists, then lim

x→c

(F(x)±G(x)) also exists.

∴lim

x→c

(h(x)−f(x))=lim

x→c

(f(x)+g(x)−f(x))=lim

x→c

g(x) exists.

For option D, take f(x)=−

x

2

cosx

and g(x)=

x

2

1

.

Limit of g(x) and f(x)=−

x

2

cosx

doesn't exist at x=0, but for

x→0

lim

f(x)+g(x) limit exists.